Businessa customer has approached a local credit union for a $20,000 1 year loan at a 10%

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Question description

A meat market manager for a large grocery store is preparing a processing plan to stock the shelves with sausage, ground meat, and jerky, which he can prepare from beef, pork and venison. Sausage and ground meat can be made of any mix of the beef, pork and venison, as long at the fat contents are below 15% for sausage and 10% for ground meat. Sausage sells for $5/pound and ground meat sells for $3/pound. Jerky, which sells or $10/pound, is made in a drying process from beef or venison. In the drying process, there is a 50% loss in weight for jerky made from beef (e.g., one pound of beef yields 0.5 pounds of beef jerky) and a 30% loss in weight for jerky made from venison. The market can sell at most 500 pounds of sausage, 1000 pounds of ground meat, and 100 pounds of jerky before their expiration dates. There are currently 1,000 pounds of beef (10% fat content), 500 pounds of pork (8% fat content), and 200 pounds of venison (2% fat content) available for processing.

Refer to Exhibit 4-3. Determine the optimal processing plan for the meat market.


2- A company blends silicon and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound.

Refer to Exhibit 4-4. Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?


3-A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000.

Refer to Exhibit 9-2. Construct a decision tree to help the credit union decide whether or not to make the loan. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

4-A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000.

Refer to Exhibit 9-2. The bank can thoroughly investigate the customer's credit record and obtain a favorable or unfavorable recommendation. If the credit report is perfectly reliable, what is the most the credit union should be willing to pay for the report?

5-A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000.

Refer to Exhibit 9-2. Should the credit union purchase the report if it costs $150?
6-A soda producer makes and sells two products, Classic Cola and Diet Cola. During the planning period, if the producer spends x1 dollars on promotion of Classic Cola, it can sell 100x10.5 cases of Classic Cola, and if it spends x2 dollars on promotion of Diet Cola, it can sell 10x20.75 cases of Diet Cola. Each case of Classic Cola sells for $12.00 and costs $0.95 to produce and ship to customers, while each case of Diet Cola sells for $12.50 and costs $1.00 to produce and ship to customers. A total of $7,500 is available for promotion during the planning period.

Refer to Exhibit 7-2. Formulate and solve a nonlinear optimization model to help this soda producer identify the best promotional strategies for its two products?

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(Top Tutor) Daniel C.
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